# An efficient iterative thresholding method for image segmentation

arXiv: https://arxiv.org/abs/1608.01431 · HTML: https://mlsanity.com/paper/1608.01431/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2016.

## Built on by (most cited first, 10 of 10)

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- [Slender Object Scene Segmentation in Remote Sensing Image Based on Learnable Morphological Skeleton with Segment Anything Model](https://mlsanity.com/paper/2411.08592/) (2024)
- [An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multi-phase Image Segmentation](https://mlsanity.com/paper/2203.09036/) (2022)
- [Topology preserving Image segmentation using the iterative convolution-thresholding method](https://mlsanity.com/paper/2503.17792/) (2025)
- [Contour Field based Elliptical Shape Prior for the Segment Anything Model](https://mlsanity.com/paper/2504.12556/) (2025)
- [A Unified Variational Framework for Deep Weakly Supervised Image Segmentation](https://mlsanity.com/paper/2607.19669/) (2026)

## Abstract (arXiv)

We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a non-local multi-phase energy. The minimization problem is solved by an iterative method. Each iteration consists of computing simple convolutions followed by a thresholding step. The algorithm is easy to implement and has the optimal complexity O(N log N) per iteration. We also show that the iterative algorithm has the total energy decaying property. We present some numerical results to show the efficiency of our method.